## [1] "Run Completed at 2018-02-07 09:51:32"
\[ Yobs_{i,j} \sim Bernoulli(N(0,1.68)) \]
Note that this is a random probability of interaction on a per observation basis. This is different than a random link model. If we are interested in a binary network, a random interaction probability model will lead to a link probability of 1-(1/2)^n in n sampling events.
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 0
## Unobserved stochastic nodes: 2073
## Total graph size: 9749
##
## Initializing model
\[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 719
## Unobserved stochastic nodes: 1354
## Total graph size: 9069
##
## Initializing model
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega_i) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect.jags")
## cat("
## model {
##
## #True interaction probability for each bird, plant
## for (i in 1:Birds){
## for(j in 1:Plants){
## logit(s[i,j])<-alpha[i,j]
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Detection Process
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation
## p[x]<-z[x] * s[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(p[x])
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## pnew[x] <- znew[x]*s[NewBird[x],NewPlant[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Logit Intercept
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 719
## Unobserved stochastic nodes: 2949
## Total graph size: 11498
##
## Initializing model
# Incorporating species occurrence
If species co-occurrence is a prerequisite for interaction, then the absence of interactions may stem either from a lack of detectability or species absence. We can jointly model the presence of species as a function of elevation and then existance of an interaction.
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega_i) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect_Elevation.jags")
## cat("
## model {
##
## #Ecological Process Model
## #True State for each bird, plant, camera
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
##
## #Occurrence
## logit(psi[i,j,k])<-alpha_occ[i] + beta_occ[i] * elevation[k] + beta2_occ[i] * elevation[k]^2
## occ[i,j,k] ~ dbern(psi[i,j,k])
##
## #Interaction
## logit(s[i,j,k])<-alpha[i,j]
##
## #Conditional probability of interaction|occurrence
## rho[i,j,k] <- s[i,j,k] * occ[i,j,k]
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Detection Process
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation, conditional on detection and occurrence.
## p[x]<-z[x] * rho[Bird[x],Plant[x],Camera[x]]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## #E[x]<-abs(Yobs[x]- s[Bird[x],Plant[x],Camera[x]])
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## pnew[x] <- znew[x]*rho[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Occurrence model
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## beta2_occ[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #Observation group prior
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive check
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 719
## Unobserved stochastic nodes: 40614
## Total graph size: 92831
##
## Initializing model
## # A tibble: 4 x 4
## # Groups: Model [4]
## Model Presence Absence p
## <chr> <int> <int> <dbl>
## 1 Random 27236 4264 86.5
## 2 Species 24570 6930 78.0
## 3 Species_Detect 726 2424 23.0
## 4 Species_Detect_Elevation 6955 24545 22.1
## [1] "True presence rate is: 8.9"
Dashed line is the observed network from the time-series.
Dissimilairty in interactions (Beta_WN from Poisot 2012) Dashed line is the observed network from the time-series. Note that this is really a measure of dissimilairty in one level (hummimngbirds), as the dissimilarity in plants is fixed by the sampling protocol. While there be a correlation between the species pool and the chosen plant to film, this is filtered by a human placing a camera at that plant, and as such isn’t a true measure of plant dissimiality.
Create a kind of venn diagram on PCA of model similarity based on per link discrepency.
## # A tibble: 17 x 3
## # Groups: Model [4]
## Model mean pair
## <chr> <dbl> <chr>
## 1 Species_Detect -1.00 Collared Inca_Pitcairnia sodiroi
## 2 Species_Detect -1.00 Gorgeted Sunangel_Palicourea lineata
## 3 Species_Detect -1.00 Purple-bibbed Whitetip_Psammisia ulbri…
## 4 Species_Detect -1.00 Tawny-bellied Hermit_Gasteranthus late…
## 5 Species_Detect_Elevation -1.00 Gorgeted Sunangel_Palicourea lineata
## 6 Species_Detect_Elevation -0.970 Purple-bibbed Whitetip_Psammisia ulbri…
## 7 Species_Detect_Elevation -0.952 Tawny-bellied Hermit_Glossoloma purpur…
## 8 Species_Detect_Elevation -0.940 Collared Inca_Macleania bullata
## 9 Species_Detect_Elevation -0.940 Tawny-bellied Hermit_Gasteranthus late…
## 10 Species -0.782 Tawny-bellied Hermit_Glossoloma purpur…
## 11 Species -0.686 Violet-tailed Sylph_Heliconia burleana
## 12 Species -0.680 Green-fronted Lancebill_Macleania bull…
## 13 Species -0.675 Violet-tailed Sylph_Psammisia ulbrichi…
## 14 Random -0.600 Stripe-throated Hermit_Palicourea line…
## 15 Random -0.590 White-whiskered Hermit_Columnea ciliata
## 16 Random -0.578 Sparkling Violetear_Columnea masterson…
## 17 Random -0.575 Collared Inca_Columnea ciliata
Without random model
TODO: What about the species that aren’t in the time series, can they be predicted by random encounter.